chap4 - Multipoles Macroscopic Media Dielectrics Henry...

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Unformatted text preview: Multipoles; Macroscopic Media; Dielectrics Henry Cavendish (1731 - 1810) December 23, 2000 Contents 1 Multipole Expansion: An Alternate Approach 2 1.1 Interpretation of the Moments . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Dipole Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2 Energy of the Charge Distribution 10 2.1 Example: Dipole Energies . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Example: Quadrupole Energies . . . . . . . . . . . . . . . . . . . . . 12 3 Dipoles in Nature: Permanent and Induced 13 3.1 Permanent Dipoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 Induced Dipoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2.1 Static Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2.2 Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4 Dielectric Materials 17 4.1 Statistical Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.1.1 Induced dipoles . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1 4.1.2 Permanent Dipoles . . . . . . . . . . . . . . . . . . . . . . . . 20 4.1.3 Both . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2 Macroscopic Electrostatics; Dielectrics . . . . . . . . . . . . . . . . . 21 4.2.1 Electric Displacement . . . . . . . . . . . . . . . . . . . . . . . 27 4.2.2 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . 29 5 Boundary-Value Problems in Dielectrics 33 5.1 Example: Point Charge Near a Boundary . . . . . . . . . . . . . . . . 35 5.2 Example: Dielectric Sphere in a Uniform Field . . . . . . . . . . . . . 40 5.2.1 The Inverse Problem . . . . . . . . . . . . . . . . . . . . . . . 43 5.3 Clausius-Mossotti equation . . . . . . . . . . . . . . . . . . . . . . . . 44 6 Electrostatic Energy in Dielectrics 46 6.1 Force on a Dielectric . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.2 Forces on a Dielectric Revisited . . . . . . . . . . . . . . . . . . . . . 52 7 Example: Dielectrophoresis 56 A Multipole Expansion: with Spherical Harmonics 64 2 In this chapter, we shall first develop the multipole expansion for the electrostatic potential and field. This is useful not only for ex- pressing the field produced by a localized distribution of charge but is also a helpful preliminary investigation for the business of describ- ing the electrostatics of materials containing a large number of charges and which are not conductors. These are called dielectrics . After de- veloping a means of describing their electrostatic properties, we shall turn to boundary value problems in systems comprising dielectrics and conductors. 1 Multipole Expansion: An Alternate Approach In this section we will develop the multipole expansion for a charge distribution by an alternate means to that used in Jackson (the method used in Jackson is discussed in the appendix to this chapter)....
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This note was uploaded on 01/08/2012 for the course PHYSICS 707 taught by Professor Electrodynamics during the Fall '11 term at LSU.

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chap4 - Multipoles Macroscopic Media Dielectrics Henry...

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